In the triangle below, what is the length of the side opposite the 60° angle? O A. 3 O B. v O C. VE OD. 6
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Answer:

The coefficient of the squared term of the equation is 1/9.

Step-by-step explanation:

We are given that the vertex of the parabola is at (-2, -3). We also know that when the y-value is -2, the x-value is -5. Using this information we want to find the cofficient of the squared term in the parabola's equation.

Since we are given the vertex, we can use the vertex form:

[tex]\displaystyle y=a(x-h)^2+k[/tex]

Where a is the leading coefficient and (h, k) is the vertex.

Since the vertex is (-2, -3), h = -2 and k = -3:

[tex]\displaystyle y=a(x-(-2))^2+(-3)[/tex]

Simplify:

[tex]y=a(x+2)^2-3[/tex]

We are also given that y = -2 when x = -5. Substitute:

[tex](-2)=a(-5+2)^2-3[/tex]

Solve for a. Simplify:

[tex]\displaystyle \begin{aligned} -2&=a(-3)^2-3\\ 1&=9a \\a&=\frac{1}{9}\end{aligned}[/tex]

Therefore, our full vertex equation is:

[tex]\displaystyle y=\frac{1}{9}(x+2)^2-3[/tex]

We can expand:

[tex]\displaystyle y=\frac{1}{9}(x^2+4x+4)-3[/tex]

Simplify:

[tex]\displaystyle y=\frac{1}{9}x^2+\frac{4}{9}x-\frac{23}{9}[/tex]

The coefficient of the squared term of the equation is 1/9.

Answer:

Letter C

Step-by-step explanation:

Given:

[tex]24x-17x[/tex] ≥ [tex]13x+15[/tex]

Combine like terms

[tex]7x[/tex] ≥ [tex]13x+15[/tex]

Subtract both sides by 13x

[tex]-6x[/tex] ≥ [tex]15[/tex]

DIvide -6 from both sides

[tex]x[/tex] ≥ [tex]-2.5[/tex]

Letter C is the answer because it is at -2.5, the arrow is facing to the right, and the dot or circle is closed to indicate that it is greater than "or equal to".

Hope this helps

Answer:

19: x=5

20: x=13

21: y= 11

     x= 11

Step-by-step explanation:

Answer:

c.12

Step-by-step explanation:

you do 33-9 which gets you 24. You then divide that by 2 so you get 12.

Answer:

The values of h = -2 and 4

The value of k = -3

Step-by-step explanation:

Putting x=5 in the given equation,

x²+(k-1)x-5=0

or, 5²+(k-1)*5-5=0

or, 25+5k-5-5=0

or, 15+5k=0

or, 5k=-15

or, k=-3

putting the value of k and the other root (h+1) in the given equation,

(h+1)²+(-3-1)(h+1)-5=0

if you solve this, you'll get h = -2 and h = 4.

Answered by GAUTHMATH

Answer:

B

Step-by-step explanation:

step

Answer:

the answer is 28.8 billion plastic bottles

Answer:

28.8 million

Step-by-step explanation:

24 hrs in one day - 1.2 M*24=28.8 M

Answer:

40 outfits possible

Step-by-step explanation:

4 shirts * 3 pairs of pants * 2 paird of shoes * 2 jackets = 40 outfits possible

Answer:my=8x

To find the inverse, flip the x and y variables and then solve for y.

x=8y

x/8=8y/8

x/8=y

Final answer: f^-1(x)=x/8

Answer:

A

Step-by-step explanation:

The formula is 5*x=4*10. Then simplify to 5*x=40. Divide both sides by 5. x=8

The domain is the span of the x-values, and the range is the span of the y-values. In each, we are looking for the smallest and largest values.

Domain: x starts at -7, and goes to infinity (we cannot see an end)

(-7, infinity)

Range: y starts at negative infinity (we cannot see where it would start), and goes to 3

(negative infinity, 3)

Hope this helps!

Answer:

the domain starts at -7 ... only one answer has the domain starting at -7

domain(-7, infinity)

Step-by-step explanation:

the domain starts at -7 ... only one answer has the domain starting at -7

Answer:

x = 1, -5.56

Step-by-step explanation:

x^2 = -7x - 8

shift -7x and -8 to the other side . Remember when u shift minus changes into plus.

x^2 + 7x + 8 = 0

using quadratic equation formula

in quadratic equation one value comes positive and other comes in negative

a = 1  , b = 7 and c = 8

taking positive sign

x = (-b + [tex]\sqrt{b^2 - 4*a*c}[/tex]) /2*a

x = (-7 + [tex]\sqrt{7^2 - 4*1*8}[/tex] ) /2*1

x = (-7 + [tex]\sqrt{49 + 32}[/tex] ) /2

x = (-7 + [tex]\sqrt{81}[/tex] )/ 2

x = -7 + 9 / 2

x = 2/2

x = 1

taking negative sign

(-b - [tex]\sqrt{b^2 - 4*a*c}[/tex] ) /2*a

x = (-7 - [tex]\sqrt{7^2 - 4*1*8}[/tex] ) /2*1

x = (-7 - [tex]\sqrt{49 - 32}[/tex] ) /2

x = -7 - [tex]\sqrt{17}[/tex] / 2

x = -7 - 4.12 / 2

x = -11.12/2

x = -5.56

therefore x = 1 , - 5.56

Answer:

[tex]x = \frac{- 7 + \sqrt{17}}{2} \ , \ x = \frac{-7 - \sqrt{17}}{2}[/tex]

Step-by-step explanation:

[tex]x^2 = - 7x - 8\\\\x^2 + 7x + 8 = 0 \\\\[/tex]

[tex]x = \frac{- b \pm \sqrt{b^2 - 4ac}}{2a}\\\\[/tex]               [tex][ \ a = 1 , \ b = 7 , \ c = 8 \ ][/tex]

[tex]x = \frac{-7 \pm \sqrt{49 - (4\times 8)}}{2} \\\\x = \frac{-7 \pm \sqrt{17}}{2} \\\\x = \frac{-7 + \sqrt{17}}{2} , \ , \frac{-7 - \sqrt{17}}{2}[/tex]

∠HGF ∠EGF

Hope this helps! :)

Answer:

24 brushes

Step-by-step explanation:

Given data

cost per brush= $19.90

Amount made =$477.60

hence the number of brushes sold is given as

Number of brushes= 477.60/19.90

Number of brushes= 477.60/19.90

Number of brushes= 24 brushes

Answer:

9.5 miles

Step-by-step explanation:

Since her route is in the shape of a triangle, total distance travelled can be determined by calculating the perimeter of a triangle.

A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees

The perimeter of a triangle = sum of the side lengths

The total distance travelled can be determined by adding the miles she rode

2.3 + 3.4 + 3.8 = 9.5 miles

Answer:

200π cm²

Step-by-step explanation:

Applying,

TSA = πrl+πr²

TSA = π(r²+rl)............. Equation 1

Where TSA = Total surface area, r = radius of the base, l = slight height of the cone

To get l we apply pythagoras theorem

From the diagram,

l² = 15²+8²

l² = 225+64

l² = 289

l = √289

l = 17 cm

Given: r = 8 cm

Substitute these values into equation 1

TSA = π(8²+17×8)

TSA = π(64+136)

TSA = π(200)

TSA = 200π cm²

Answer:

OK , so I'll follow all your instructions:

x² + 12x - x + 24 = 0

x² + 11x + 24 = 0.......product = 24, sum= 11 & factors = 3 & 8

(x² + 3x ) (+ 8x + 24) =0

x ( x + 3) + 8 ( x + 3)=0

( x + 3 ) ( x + 8)=0

x +3 = 0 or x + 8= 0

x = -3. or x = -8

Answer:

The factor is polynomial

Step-by-step explanation:

trust me broski

Answer: 12.48

Step-by-step explanation:

38x38+bxb=40x40

1444+b=1600

1600-1444=156

[tex]\sqrt156[/tex]=12.48

The base of the house is 12.48 foot far from the foot of the ladder.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

|AC|^2 = |AB|^2 + |BC|^2    

It is given that A 40-foot ladder reaches 38 feet up the side of a house.

We need to find that How far from the base of the house is the foot of the ladder.

Using Pythagoras theorem, we get;

[tex]38^2 + b^2 =40^2\\\\1444 + b^2 = 1600\\ \\b^2 = 1600 - 1444 \\\\b^2= 156\\\\b = 12.48[/tex]

Therefore, the base of the house is 12.48 foot far from the foot of the ladder.

Learn more about Pythagoras theorem;

https://brainly.com/question/343682

#SPJ2

Given:

The expression is:

[tex]8x^4-2x[/tex]

To find:

The coefficient and the exponent for each term of the given expression.

Solution:

Coefficients: In the product of s number and a variable, the number is coefficient of the variable.

Exponent: The number in the power is called exponent.

We have,

[tex]8x^4-2x[/tex]

Here, the terms are [tex]8x^4,-2x[/tex].

For the term [tex]8x^4[/tex], the coefficient is 8 and the exponent is 4.

For the term [tex]-2x[/tex], the coefficient is -2 and the exponent is 1.

Therefore, the coefficients are 8 and -2, and the exponent are 4 and 1.

Answer: 28

Step-by-step explanation: 5(4)-4(-2) which is 20+8 and that is 28.

Answer:

reading books (458), science books (957), mathematics books (1054)

Step-by-step explanation:

458 is less than 957 and 1054, while 957 is less than 1054 but more than 458, and 1054 is more than 957 and 458.

458<957<1054

[tex]\longrightarrow{\green{x\:=\:5}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

➝[tex]\: \frac{3x}{5} = \frac{x + 1}{2} [/tex]

➝[tex]\:2 \times 3x = 5(x + 1)[/tex]

➝[tex]\:6x = 5x + 5[/tex]

➝[tex]\:6x - 5x = 5[/tex]

➝[tex]\:x = 5[/tex]

✒[tex] \:\frac{3 \times 5}{5} = \frac{5 + 1}{2} [/tex]

✒[tex]\: \frac{15}{5} = \frac{6}{2} [/tex]

✒[tex]\:3 = 3[/tex]

✒[tex]\:L. H. S. =R. H. S. [/tex]

Hence verified.

[tex]\bold{ \green{ \star{ \orange{Mystique35☂}}}}⋆[/tex]

Answer:

100 is answer for math picture

Answer: 80

Step-by-step explanation:

180-100 = 80, y=80

Answer:

[tex]x=9.91[/tex]

Step-by-step explanation:

[tex]11x-3=106[/tex]

      [tex]+3[/tex]       [tex]+3[/tex]

[tex]11x=109[/tex]

[tex]/11[/tex]       [tex]/11[/tex]

[tex]x=9.91[/tex]

Answer:

£7

Step-by-step explanation:

x - .2x = £5.60

.8(x) = £5.6

x= £5.6/.8

Answer:

In 5 years I will have $ 1,151.71.

Step-by-step explanation:

To determine, if I put 700 into a savings account that's earns 1% interest compound monthly, how much will I have in 5 years, the following calculation must be performed:

700 x (1 + 0.01 / 12) ^ 12x5 = X

700 x (1 + 0.008333) ^ 60 = X

700 x 1.64530 = X

1,151.71 = X

Therefore, in 5 years I will have $ 1,151.71.